#include <iostream>
#include "../../../src/FTensor.hpp"
#include "../test_for_zero.hpp"
using namespace FTensor;
using namespace std;

void test_T4ddg_01(const Tensor2_symmetric<double,3> &t2s_2,
                   const Tensor2_symmetric<double,3> &t2s_3,
                   const Tensor3_dg<double,3,3> &t3dg_2,
                   const Tensor3_dg<double,3,3> &t3dg_3)
{
  Index<'i',3> i;
  Index<'j',3> j;
  Index<'k',3> k;
  Index<'l',3> l;
  Index<'m',3> m;
  Index<'n',3> n;

  Number<0> N0;
  Number<1> N1;
  Number<2> N2;

  Tensor4_ddg<double,3,3> t4ddg_1, t4ddg_2, t4ddg_3;

  t4ddg_1(i,j,l,m)=t3dg_2(i,j,k)*t3dg_3(l,m,k);
  test_for_zero(t4ddg_1(0,0,0,0) - (t3dg_2(0,0,0)*t3dg_3(0,0,0)
				    + t3dg_2(0,0,1)*t3dg_3(0,0,1)
				    + t3dg_2(0,0,2)*t3dg_3(0,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,0,0,0)");
  test_for_zero(t4ddg_1(0,0,0,1) - (t3dg_2(0,0,0)*t3dg_3(0,1,0)
				    + t3dg_2(0,0,1)*t3dg_3(0,1,1)
				    + t3dg_2(0,0,2)*t3dg_3(0,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,0,0,1)");
  test_for_zero(t4ddg_1(0,0,0,2) - (t3dg_2(0,0,0)*t3dg_3(0,2,0)
				    + t3dg_2(0,0,1)*t3dg_3(0,2,1)
				    + t3dg_2(0,0,2)*t3dg_3(0,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,0,0,2)");
  test_for_zero(t4ddg_1(0,0,1,0) - (t3dg_2(0,0,0)*t3dg_3(1,0,0)
				    + t3dg_2(0,0,1)*t3dg_3(1,0,1)
				    + t3dg_2(0,0,2)*t3dg_3(1,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,0,1,0)");
  test_for_zero(t4ddg_1(0,0,1,1) - (t3dg_2(0,0,0)*t3dg_3(1,1,0)
				    + t3dg_2(0,0,1)*t3dg_3(1,1,1)
				    + t3dg_2(0,0,2)*t3dg_3(1,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,0,1,1)");
  test_for_zero(t4ddg_1(0,0,1,2) - (t3dg_2(0,0,0)*t3dg_3(1,2,0)
				    + t3dg_2(0,0,1)*t3dg_3(1,2,1)
				    + t3dg_2(0,0,2)*t3dg_3(1,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,0,1,2)");
  test_for_zero(t4ddg_1(0,0,2,0) - (t3dg_2(0,0,0)*t3dg_3(2,0,0)
				    + t3dg_2(0,0,1)*t3dg_3(2,0,1)
				    + t3dg_2(0,0,2)*t3dg_3(2,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,0,2,0)");
  test_for_zero(t4ddg_1(0,0,2,1) - (t3dg_2(0,0,0)*t3dg_3(2,1,0)
				    + t3dg_2(0,0,1)*t3dg_3(2,1,1)
				    + t3dg_2(0,0,2)*t3dg_3(2,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,0,2,1)");
  test_for_zero(t4ddg_1(0,0,2,2) - (t3dg_2(0,0,0)*t3dg_3(2,2,0)
				    + t3dg_2(0,0,1)*t3dg_3(2,2,1)
				    + t3dg_2(0,0,2)*t3dg_3(2,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,0,2,2)");
  test_for_zero(t4ddg_1(0,1,0,0) - (t3dg_2(0,1,0)*t3dg_3(0,0,0)
				    + t3dg_2(0,1,1)*t3dg_3(0,0,1)
				    + t3dg_2(0,1,2)*t3dg_3(0,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,1,0,0)");
  test_for_zero(t4ddg_1(0,1,0,1) - (t3dg_2(0,1,0)*t3dg_3(0,1,0)
				    + t3dg_2(0,1,1)*t3dg_3(0,1,1)
				    + t3dg_2(0,1,2)*t3dg_3(0,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,1,0,1)");
  test_for_zero(t4ddg_1(0,1,0,2) - (t3dg_2(0,1,0)*t3dg_3(0,2,0)
				    + t3dg_2(0,1,1)*t3dg_3(0,2,1)
				    + t3dg_2(0,1,2)*t3dg_3(0,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,1,0,2)");
  test_for_zero(t4ddg_1(0,1,1,0) - (t3dg_2(0,1,0)*t3dg_3(1,0,0)
				    + t3dg_2(0,1,1)*t3dg_3(1,0,1)
				    + t3dg_2(0,1,2)*t3dg_3(1,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,1,1,0)");
  test_for_zero(t4ddg_1(0,1,1,1) - (t3dg_2(0,1,0)*t3dg_3(1,1,0)
				    + t3dg_2(0,1,1)*t3dg_3(1,1,1)
				    + t3dg_2(0,1,2)*t3dg_3(1,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,1,1,1)");
  test_for_zero(t4ddg_1(0,1,1,2) - (t3dg_2(0,1,0)*t3dg_3(1,2,0)
				    + t3dg_2(0,1,1)*t3dg_3(1,2,1)
				    + t3dg_2(0,1,2)*t3dg_3(1,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,1,1,2)");
  test_for_zero(t4ddg_1(0,1,2,0) - (t3dg_2(0,1,0)*t3dg_3(2,0,0)
				    + t3dg_2(0,1,1)*t3dg_3(2,0,1)
				    + t3dg_2(0,1,2)*t3dg_3(2,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,1,2,0)");
  test_for_zero(t4ddg_1(0,1,2,1) - (t3dg_2(0,1,0)*t3dg_3(2,1,0)
				    + t3dg_2(0,1,1)*t3dg_3(2,1,1)
				    + t3dg_2(0,1,2)*t3dg_3(2,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,1,2,1)");
  test_for_zero(t4ddg_1(0,1,2,2) - (t3dg_2(0,1,0)*t3dg_3(2,2,0)
				    + t3dg_2(0,1,1)*t3dg_3(2,2,1)
				    + t3dg_2(0,1,2)*t3dg_3(2,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,1,2,2)");
  test_for_zero(t4ddg_1(0,2,0,0) - (t3dg_2(0,2,0)*t3dg_3(0,0,0)
				    + t3dg_2(0,2,1)*t3dg_3(0,0,1)
				    + t3dg_2(0,2,2)*t3dg_3(0,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,2,0,0)");
  test_for_zero(t4ddg_1(0,2,0,1) - (t3dg_2(0,2,0)*t3dg_3(0,1,0)
				    + t3dg_2(0,2,1)*t3dg_3(0,1,1)
				    + t3dg_2(0,2,2)*t3dg_3(0,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,2,0,1)");
  test_for_zero(t4ddg_1(0,2,0,2) - (t3dg_2(0,2,0)*t3dg_3(0,2,0)
				    + t3dg_2(0,2,1)*t3dg_3(0,2,1)
				    + t3dg_2(0,2,2)*t3dg_3(0,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,2,0,2)");
  test_for_zero(t4ddg_1(0,2,1,0) - (t3dg_2(0,2,0)*t3dg_3(1,0,0)
				    + t3dg_2(0,2,1)*t3dg_3(1,0,1)
				    + t3dg_2(0,2,2)*t3dg_3(1,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,2,1,0)");
  test_for_zero(t4ddg_1(0,2,1,1) - (t3dg_2(0,2,0)*t3dg_3(1,1,0)
				    + t3dg_2(0,2,1)*t3dg_3(1,1,1)
				    + t3dg_2(0,2,2)*t3dg_3(1,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,2,1,1)");
  test_for_zero(t4ddg_1(0,2,1,2) - (t3dg_2(0,2,0)*t3dg_3(1,2,0)
				    + t3dg_2(0,2,1)*t3dg_3(1,2,1)
				    + t3dg_2(0,2,2)*t3dg_3(1,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,2,1,2)");
  test_for_zero(t4ddg_1(0,2,2,0) - (t3dg_2(0,2,0)*t3dg_3(2,0,0)
				    + t3dg_2(0,2,1)*t3dg_3(2,0,1)
				    + t3dg_2(0,2,2)*t3dg_3(2,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,2,2,0)");
  test_for_zero(t4ddg_1(0,2,2,1) - (t3dg_2(0,2,0)*t3dg_3(2,1,0)
				    + t3dg_2(0,2,1)*t3dg_3(2,1,1)
				    + t3dg_2(0,2,2)*t3dg_3(2,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,2,2,1)");
  test_for_zero(t4ddg_1(0,2,2,2) - (t3dg_2(0,2,0)*t3dg_3(2,2,0)
				    + t3dg_2(0,2,1)*t3dg_3(2,2,1)
				    + t3dg_2(0,2,2)*t3dg_3(2,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(0,2,2,2)");
  test_for_zero(t4ddg_1(1,0,0,0) - (t3dg_2(1,0,0)*t3dg_3(0,0,0)
				    + t3dg_2(1,0,1)*t3dg_3(0,0,1)
				    + t3dg_2(1,0,2)*t3dg_3(0,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,0,0,0)");
  test_for_zero(t4ddg_1(1,0,0,1) - (t3dg_2(1,0,0)*t3dg_3(0,1,0)
				    + t3dg_2(1,0,1)*t3dg_3(0,1,1)
				    + t3dg_2(1,0,2)*t3dg_3(0,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,0,0,1)");
  test_for_zero(t4ddg_1(1,0,0,2) - (t3dg_2(1,0,0)*t3dg_3(0,2,0)
				    + t3dg_2(1,0,1)*t3dg_3(0,2,1)
				    + t3dg_2(1,0,2)*t3dg_3(0,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,0,0,2)");
  test_for_zero(t4ddg_1(1,0,1,0) - (t3dg_2(1,0,0)*t3dg_3(1,0,0)
				    + t3dg_2(1,0,1)*t3dg_3(1,0,1)
				    + t3dg_2(1,0,2)*t3dg_3(1,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,0,1,0)");
  test_for_zero(t4ddg_1(1,0,1,1) - (t3dg_2(1,0,0)*t3dg_3(1,1,0)
				    + t3dg_2(1,0,1)*t3dg_3(1,1,1)
				    + t3dg_2(1,0,2)*t3dg_3(1,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,0,1,1)");
  test_for_zero(t4ddg_1(1,0,1,2) - (t3dg_2(1,0,0)*t3dg_3(1,2,0)
				    + t3dg_2(1,0,1)*t3dg_3(1,2,1)
				    + t3dg_2(1,0,2)*t3dg_3(1,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,0,1,2)");
  test_for_zero(t4ddg_1(1,0,2,0) - (t3dg_2(1,0,0)*t3dg_3(2,0,0)
				    + t3dg_2(1,0,1)*t3dg_3(2,0,1)
				    + t3dg_2(1,0,2)*t3dg_3(2,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,0,2,0)");
  test_for_zero(t4ddg_1(1,0,2,1) - (t3dg_2(1,0,0)*t3dg_3(2,1,0)
				    + t3dg_2(1,0,1)*t3dg_3(2,1,1)
				    + t3dg_2(1,0,2)*t3dg_3(2,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,0,2,1)");
  test_for_zero(t4ddg_1(1,0,2,2) - (t3dg_2(1,0,0)*t3dg_3(2,2,0)
				    + t3dg_2(1,0,1)*t3dg_3(2,2,1)
				    + t3dg_2(1,0,2)*t3dg_3(2,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,0,2,2)");
  test_for_zero(t4ddg_1(1,1,0,0) - (t3dg_2(1,1,0)*t3dg_3(0,0,0)
				    + t3dg_2(1,1,1)*t3dg_3(0,0,1)
				    + t3dg_2(1,1,2)*t3dg_3(0,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,1,0,0)");
  test_for_zero(t4ddg_1(1,1,0,1) - (t3dg_2(1,1,0)*t3dg_3(0,1,0)
				    + t3dg_2(1,1,1)*t3dg_3(0,1,1)
				    + t3dg_2(1,1,2)*t3dg_3(0,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,1,0,1)");
  test_for_zero(t4ddg_1(1,1,0,2) - (t3dg_2(1,1,0)*t3dg_3(0,2,0)
				    + t3dg_2(1,1,1)*t3dg_3(0,2,1)
				    + t3dg_2(1,1,2)*t3dg_3(0,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,1,0,2)");
  test_for_zero(t4ddg_1(1,1,1,0) - (t3dg_2(1,1,0)*t3dg_3(1,0,0)
				    + t3dg_2(1,1,1)*t3dg_3(1,0,1)
				    + t3dg_2(1,1,2)*t3dg_3(1,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,1,1,0)");
  test_for_zero(t4ddg_1(1,1,1,1) - (t3dg_2(1,1,0)*t3dg_3(1,1,0)
				    + t3dg_2(1,1,1)*t3dg_3(1,1,1)
				    + t3dg_2(1,1,2)*t3dg_3(1,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,1,1,1)");
  test_for_zero(t4ddg_1(1,1,1,2) - (t3dg_2(1,1,0)*t3dg_3(1,2,0)
				    + t3dg_2(1,1,1)*t3dg_3(1,2,1)
				    + t3dg_2(1,1,2)*t3dg_3(1,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,1,1,2)");
  test_for_zero(t4ddg_1(1,1,2,0) - (t3dg_2(1,1,0)*t3dg_3(2,0,0)
				    + t3dg_2(1,1,1)*t3dg_3(2,0,1)
				    + t3dg_2(1,1,2)*t3dg_3(2,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,1,2,0)");
  test_for_zero(t4ddg_1(1,1,2,1) - (t3dg_2(1,1,0)*t3dg_3(2,1,0)
				    + t3dg_2(1,1,1)*t3dg_3(2,1,1)
				    + t3dg_2(1,1,2)*t3dg_3(2,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,1,2,1)");
  test_for_zero(t4ddg_1(1,1,2,2) - (t3dg_2(1,1,0)*t3dg_3(2,2,0)
				    + t3dg_2(1,1,1)*t3dg_3(2,2,1)
				    + t3dg_2(1,1,2)*t3dg_3(2,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,1,2,2)");
  test_for_zero(t4ddg_1(1,2,0,0) - (t3dg_2(1,2,0)*t3dg_3(0,0,0)
				    + t3dg_2(1,2,1)*t3dg_3(0,0,1)
				    + t3dg_2(1,2,2)*t3dg_3(0,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,2,0,0)");
  test_for_zero(t4ddg_1(1,2,0,1) - (t3dg_2(1,2,0)*t3dg_3(0,1,0)
				    + t3dg_2(1,2,1)*t3dg_3(0,1,1)
				    + t3dg_2(1,2,2)*t3dg_3(0,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,2,0,1)");
  test_for_zero(t4ddg_1(1,2,0,2) - (t3dg_2(1,2,0)*t3dg_3(0,2,0)
				    + t3dg_2(1,2,1)*t3dg_3(0,2,1)
				    + t3dg_2(1,2,2)*t3dg_3(0,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,2,0,2)");
  test_for_zero(t4ddg_1(1,2,1,0) - (t3dg_2(1,2,0)*t3dg_3(1,0,0)
				    + t3dg_2(1,2,1)*t3dg_3(1,0,1)
				    + t3dg_2(1,2,2)*t3dg_3(1,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,2,1,0)");
  test_for_zero(t4ddg_1(1,2,1,1) - (t3dg_2(1,2,0)*t3dg_3(1,1,0)
				    + t3dg_2(1,2,1)*t3dg_3(1,1,1)
				    + t3dg_2(1,2,2)*t3dg_3(1,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,2,1,1)");
  test_for_zero(t4ddg_1(1,2,1,2) - (t3dg_2(1,2,0)*t3dg_3(1,2,0)
				    + t3dg_2(1,2,1)*t3dg_3(1,2,1)
				    + t3dg_2(1,2,2)*t3dg_3(1,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,2,1,2)");
  test_for_zero(t4ddg_1(1,2,2,0) - (t3dg_2(1,2,0)*t3dg_3(2,0,0)
				    + t3dg_2(1,2,1)*t3dg_3(2,0,1)
				    + t3dg_2(1,2,2)*t3dg_3(2,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,2,2,0)");
  test_for_zero(t4ddg_1(1,2,2,1) - (t3dg_2(1,2,0)*t3dg_3(2,1,0)
				    + t3dg_2(1,2,1)*t3dg_3(2,1,1)
				    + t3dg_2(1,2,2)*t3dg_3(2,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,2,2,1)");
  test_for_zero(t4ddg_1(1,2,2,2) - (t3dg_2(1,2,0)*t3dg_3(2,2,0)
				    + t3dg_2(1,2,1)*t3dg_3(2,2,1)
				    + t3dg_2(1,2,2)*t3dg_3(2,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(1,2,2,2)");
  test_for_zero(t4ddg_1(2,0,0,0) - (t3dg_2(2,0,0)*t3dg_3(0,0,0)
				    + t3dg_2(2,0,1)*t3dg_3(0,0,1)
				    + t3dg_2(2,0,2)*t3dg_3(0,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,0,0,0)");
  test_for_zero(t4ddg_1(2,0,0,1) - (t3dg_2(2,0,0)*t3dg_3(0,1,0)
				    + t3dg_2(2,0,1)*t3dg_3(0,1,1)
				    + t3dg_2(2,0,2)*t3dg_3(0,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,0,0,1)");
  test_for_zero(t4ddg_1(2,0,0,2) - (t3dg_2(2,0,0)*t3dg_3(0,2,0)
				    + t3dg_2(2,0,1)*t3dg_3(0,2,1)
				    + t3dg_2(2,0,2)*t3dg_3(0,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,0,0,2)");
  test_for_zero(t4ddg_1(2,0,1,0) - (t3dg_2(2,0,0)*t3dg_3(1,0,0)
				    + t3dg_2(2,0,1)*t3dg_3(1,0,1)
				    + t3dg_2(2,0,2)*t3dg_3(1,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,0,1,0)");
  test_for_zero(t4ddg_1(2,0,1,1) - (t3dg_2(2,0,0)*t3dg_3(1,1,0)
				    + t3dg_2(2,0,1)*t3dg_3(1,1,1)
				    + t3dg_2(2,0,2)*t3dg_3(1,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,0,1,1)");
  test_for_zero(t4ddg_1(2,0,1,2) - (t3dg_2(2,0,0)*t3dg_3(1,2,0)
				    + t3dg_2(2,0,1)*t3dg_3(1,2,1)
				    + t3dg_2(2,0,2)*t3dg_3(1,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,0,1,2)");
  test_for_zero(t4ddg_1(2,0,2,0) - (t3dg_2(2,0,0)*t3dg_3(2,0,0)
				    + t3dg_2(2,0,1)*t3dg_3(2,0,1)
				    + t3dg_2(2,0,2)*t3dg_3(2,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,0,2,0)");
  test_for_zero(t4ddg_1(2,0,2,1) - (t3dg_2(2,0,0)*t3dg_3(2,1,0)
				    + t3dg_2(2,0,1)*t3dg_3(2,1,1)
				    + t3dg_2(2,0,2)*t3dg_3(2,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,0,2,1)");
  test_for_zero(t4ddg_1(2,0,2,2) - (t3dg_2(2,0,0)*t3dg_3(2,2,0)
				    + t3dg_2(2,0,1)*t3dg_3(2,2,1)
				    + t3dg_2(2,0,2)*t3dg_3(2,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,0,2,2)");
  test_for_zero(t4ddg_1(2,1,0,0) - (t3dg_2(2,1,0)*t3dg_3(0,0,0)
				    + t3dg_2(2,1,1)*t3dg_3(0,0,1)
				    + t3dg_2(2,1,2)*t3dg_3(0,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,1,0,0)");
  test_for_zero(t4ddg_1(2,1,0,1) - (t3dg_2(2,1,0)*t3dg_3(0,1,0)
				    + t3dg_2(2,1,1)*t3dg_3(0,1,1)
				    + t3dg_2(2,1,2)*t3dg_3(0,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,1,0,1)");
  test_for_zero(t4ddg_1(2,1,0,2) - (t3dg_2(2,1,0)*t3dg_3(0,2,0)
				    + t3dg_2(2,1,1)*t3dg_3(0,2,1)
				    + t3dg_2(2,1,2)*t3dg_3(0,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,1,0,2)");
  test_for_zero(t4ddg_1(2,1,1,0) - (t3dg_2(2,1,0)*t3dg_3(1,0,0)
				    + t3dg_2(2,1,1)*t3dg_3(1,0,1)
				    + t3dg_2(2,1,2)*t3dg_3(1,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,1,1,0)");
  test_for_zero(t4ddg_1(2,1,1,1) - (t3dg_2(2,1,0)*t3dg_3(1,1,0)
				    + t3dg_2(2,1,1)*t3dg_3(1,1,1)
				    + t3dg_2(2,1,2)*t3dg_3(1,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,1,1,1)");
  test_for_zero(t4ddg_1(2,1,1,2) - (t3dg_2(2,1,0)*t3dg_3(1,2,0)
				    + t3dg_2(2,1,1)*t3dg_3(1,2,1)
				    + t3dg_2(2,1,2)*t3dg_3(1,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,1,1,2)");
  test_for_zero(t4ddg_1(2,1,2,0) - (t3dg_2(2,1,0)*t3dg_3(2,0,0)
				    + t3dg_2(2,1,1)*t3dg_3(2,0,1)
				    + t3dg_2(2,1,2)*t3dg_3(2,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,1,2,0)");
  test_for_zero(t4ddg_1(2,1,2,1) - (t3dg_2(2,1,0)*t3dg_3(2,1,0)
				    + t3dg_2(2,1,1)*t3dg_3(2,1,1)
				    + t3dg_2(2,1,2)*t3dg_3(2,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,1,2,1)");
  test_for_zero(t4ddg_1(2,1,2,2) - (t3dg_2(2,1,0)*t3dg_3(2,2,0)
				    + t3dg_2(2,1,1)*t3dg_3(2,2,1)
				    + t3dg_2(2,1,2)*t3dg_3(2,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,1,2,2)");
  test_for_zero(t4ddg_1(2,2,0,0) - (t3dg_2(2,2,0)*t3dg_3(0,0,0)
				    + t3dg_2(2,2,1)*t3dg_3(0,0,1)
				    + t3dg_2(2,2,2)*t3dg_3(0,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,2,0,0)");
  test_for_zero(t4ddg_1(2,2,0,1) - (t3dg_2(2,2,0)*t3dg_3(0,1,0)
				    + t3dg_2(2,2,1)*t3dg_3(0,1,1)
				    + t3dg_2(2,2,2)*t3dg_3(0,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,2,0,1)");
  test_for_zero(t4ddg_1(2,2,0,2) - (t3dg_2(2,2,0)*t3dg_3(0,2,0)
				    + t3dg_2(2,2,1)*t3dg_3(0,2,1)
				    + t3dg_2(2,2,2)*t3dg_3(0,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,2,0,2)");
  test_for_zero(t4ddg_1(2,2,1,0) - (t3dg_2(2,2,0)*t3dg_3(1,0,0)
				    + t3dg_2(2,2,1)*t3dg_3(1,0,1)
				    + t3dg_2(2,2,2)*t3dg_3(1,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,2,1,0)");
  test_for_zero(t4ddg_1(2,2,1,1) - (t3dg_2(2,2,0)*t3dg_3(1,1,0)
				    + t3dg_2(2,2,1)*t3dg_3(1,1,1)
				    + t3dg_2(2,2,2)*t3dg_3(1,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,2,1,1)");
  test_for_zero(t4ddg_1(2,2,1,2) - (t3dg_2(2,2,0)*t3dg_3(1,2,0)
				    + t3dg_2(2,2,1)*t3dg_3(1,2,1)
				    + t3dg_2(2,2,2)*t3dg_3(1,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,2,1,2)");
  test_for_zero(t4ddg_1(2,2,2,0) - (t3dg_2(2,2,0)*t3dg_3(2,0,0)
				    + t3dg_2(2,2,1)*t3dg_3(2,0,1)
				    + t3dg_2(2,2,2)*t3dg_3(2,0,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,2,2,0)");
  test_for_zero(t4ddg_1(2,2,2,1) - (t3dg_2(2,2,0)*t3dg_3(2,1,0)
				    + t3dg_2(2,2,1)*t3dg_3(2,1,1)
				    + t3dg_2(2,2,2)*t3dg_3(2,1,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,2,2,1)");
  test_for_zero(t4ddg_1(2,2,2,2) - (t3dg_2(2,2,0)*t3dg_3(2,2,0)
				    + t3dg_2(2,2,1)*t3dg_3(2,2,1)
				    + t3dg_2(2,2,2)*t3dg_3(2,2,2))
		,"T3dg(i,j,k)*T3dg(l,m,k)(2,2,2,2)");

  t4ddg_2(i,j,l,m)=t2s_2(i,j)*t2s_3(l,m);
  t4ddg_3(i,j,l,m)=t2s_3(i,j)*t2s_2(l,m);
  test_for_zero(t4ddg_2(0,0,0,0) - (t2s_2(0,0)*t2s_3(0,0))
		,"T2s(i,j)*T2s(l,m)(0,0,0,0)");
  test_for_zero(t4ddg_2(0,0,0,1) - (t2s_2(0,0)*t2s_3(0,1))
		,"T2s(i,j)*T2s(l,m)(0,0,0,1)");
  test_for_zero(t4ddg_2(0,0,0,2) - (t2s_2(0,0)*t2s_3(0,2))
		,"T2s(i,j)*T2s(l,m)(0,0,0,2)");
  test_for_zero(t4ddg_2(0,0,1,0) - (t2s_2(0,0)*t2s_3(1,0))
		,"T2s(i,j)*T2s(l,m)(0,0,1,0)");
  test_for_zero(t4ddg_2(0,0,1,1) - (t2s_2(0,0)*t2s_3(1,1))
		,"T2s(i,j)*T2s(l,m)(0,0,1,1)");
  test_for_zero(t4ddg_2(0,0,1,2) - (t2s_2(0,0)*t2s_3(1,2))
		,"T2s(i,j)*T2s(l,m)(0,0,1,2)");
  test_for_zero(t4ddg_2(0,0,2,0) - (t2s_2(0,0)*t2s_3(2,0))
		,"T2s(i,j)*T2s(l,m)(0,0,2,0)");
  test_for_zero(t4ddg_2(0,0,2,1) - (t2s_2(0,0)*t2s_3(2,1))
		,"T2s(i,j)*T2s(l,m)(0,0,2,1)");
  test_for_zero(t4ddg_2(0,0,2,2) - (t2s_2(0,0)*t2s_3(2,2))
		,"T2s(i,j)*T2s(l,m)(0,0,2,2)");
  test_for_zero(t4ddg_2(0,1,0,0) - (t2s_2(0,1)*t2s_3(0,0))
		,"T2s(i,j)*T2s(l,m)(0,1,0,0)");
  test_for_zero(t4ddg_2(0,1,0,1) - (t2s_2(0,1)*t2s_3(0,1))
		,"T2s(i,j)*T2s(l,m)(0,1,0,1)");
  test_for_zero(t4ddg_2(0,1,0,2) - (t2s_2(0,1)*t2s_3(0,2))
		,"T2s(i,j)*T2s(l,m)(0,1,0,2)");
  test_for_zero(t4ddg_2(0,1,1,0) - (t2s_2(0,1)*t2s_3(1,0))
		,"T2s(i,j)*T2s(l,m)(0,1,1,0)");
  test_for_zero(t4ddg_2(0,1,1,1) - (t2s_2(0,1)*t2s_3(1,1))
		,"T2s(i,j)*T2s(l,m)(0,1,1,1)");
  test_for_zero(t4ddg_2(0,1,1,2) - (t2s_2(0,1)*t2s_3(1,2))
		,"T2s(i,j)*T2s(l,m)(0,1,1,2)");
  test_for_zero(t4ddg_2(0,1,2,0) - (t2s_2(0,1)*t2s_3(2,0))
		,"T2s(i,j)*T2s(l,m)(0,1,2,0)");
  test_for_zero(t4ddg_2(0,1,2,1) - (t2s_2(0,1)*t2s_3(2,1))
		,"T2s(i,j)*T2s(l,m)(0,1,2,1)");
  test_for_zero(t4ddg_2(0,1,2,2) - (t2s_2(0,1)*t2s_3(2,2))
		,"T2s(i,j)*T2s(l,m)(0,1,2,2)");
  test_for_zero(t4ddg_2(0,2,0,0) - (t2s_2(0,2)*t2s_3(0,0))
		,"T2s(i,j)*T2s(l,m)(0,2,0,0)");
  test_for_zero(t4ddg_2(0,2,0,1) - (t2s_2(0,2)*t2s_3(0,1))
		,"T2s(i,j)*T2s(l,m)(0,2,0,1)");
  test_for_zero(t4ddg_2(0,2,0,2) - (t2s_2(0,2)*t2s_3(0,2))
		,"T2s(i,j)*T2s(l,m)(0,2,0,2)");
  test_for_zero(t4ddg_2(0,2,1,0) - (t2s_2(0,2)*t2s_3(1,0))
		,"T2s(i,j)*T2s(l,m)(0,2,1,0)");
  test_for_zero(t4ddg_2(0,2,1,1) - (t2s_2(0,2)*t2s_3(1,1))
		,"T2s(i,j)*T2s(l,m)(0,2,1,1)");
  test_for_zero(t4ddg_2(0,2,1,2) - (t2s_2(0,2)*t2s_3(1,2))
		,"T2s(i,j)*T2s(l,m)(0,2,1,2)");
  test_for_zero(t4ddg_2(0,2,2,0) - (t2s_2(0,2)*t2s_3(2,0))
		,"T2s(i,j)*T2s(l,m)(0,2,2,0)");
  test_for_zero(t4ddg_2(0,2,2,1) - (t2s_2(0,2)*t2s_3(2,1))
		,"T2s(i,j)*T2s(l,m)(0,2,2,1)");
  test_for_zero(t4ddg_2(0,2,2,2) - (t2s_2(0,2)*t2s_3(2,2))
		,"T2s(i,j)*T2s(l,m)(0,2,2,2)");
  test_for_zero(t4ddg_2(1,0,0,0) - (t2s_2(1,0)*t2s_3(0,0))
		,"T2s(i,j)*T2s(l,m)(1,0,0,0)");
  test_for_zero(t4ddg_2(1,0,0,1) - (t2s_2(1,0)*t2s_3(0,1))
		,"T2s(i,j)*T2s(l,m)(1,0,0,1)");
  test_for_zero(t4ddg_2(1,0,0,2) - (t2s_2(1,0)*t2s_3(0,2))
		,"T2s(i,j)*T2s(l,m)(1,0,0,2)");
  test_for_zero(t4ddg_2(1,0,1,0) - (t2s_2(1,0)*t2s_3(1,0))
		,"T2s(i,j)*T2s(l,m)(1,0,1,0)");
  test_for_zero(t4ddg_2(1,0,1,1) - (t2s_2(1,0)*t2s_3(1,1))
		,"T2s(i,j)*T2s(l,m)(1,0,1,1)");
  test_for_zero(t4ddg_2(1,0,1,2) - (t2s_2(1,0)*t2s_3(1,2))
		,"T2s(i,j)*T2s(l,m)(1,0,1,2)");
  test_for_zero(t4ddg_2(1,0,2,0) - (t2s_2(1,0)*t2s_3(2,0))
		,"T2s(i,j)*T2s(l,m)(1,0,2,0)");
  test_for_zero(t4ddg_2(1,0,2,1) - (t2s_2(1,0)*t2s_3(2,1))
		,"T2s(i,j)*T2s(l,m)(1,0,2,1)");
  test_for_zero(t4ddg_2(1,0,2,2) - (t2s_2(1,0)*t2s_3(2,2))
		,"T2s(i,j)*T2s(l,m)(1,0,2,2)");
  test_for_zero(t4ddg_2(1,1,0,0) - (t2s_2(1,1)*t2s_3(0,0))
		,"T2s(i,j)*T2s(l,m)(1,1,0,0)");
  test_for_zero(t4ddg_2(1,1,0,1) - (t2s_2(1,1)*t2s_3(0,1))
		,"T2s(i,j)*T2s(l,m)(1,1,0,1)");
  test_for_zero(t4ddg_2(1,1,0,2) - (t2s_2(1,1)*t2s_3(0,2))
		,"T2s(i,j)*T2s(l,m)(1,1,0,2)");
  test_for_zero(t4ddg_2(1,1,1,0) - (t2s_2(1,1)*t2s_3(1,0))
		,"T2s(i,j)*T2s(l,m)(1,1,1,0)");
  test_for_zero(t4ddg_2(1,1,1,1) - (t2s_2(1,1)*t2s_3(1,1))
		,"T2s(i,j)*T2s(l,m)(1,1,1,1)");
  test_for_zero(t4ddg_2(1,1,1,2) - (t2s_2(1,1)*t2s_3(1,2))
		,"T2s(i,j)*T2s(l,m)(1,1,1,2)");
  test_for_zero(t4ddg_2(1,1,2,0) - (t2s_2(1,1)*t2s_3(2,0))
		,"T2s(i,j)*T2s(l,m)(1,1,2,0)");
  test_for_zero(t4ddg_2(1,1,2,1) - (t2s_2(1,1)*t2s_3(2,1))
		,"T2s(i,j)*T2s(l,m)(1,1,2,1)");
  test_for_zero(t4ddg_2(1,1,2,2) - (t2s_2(1,1)*t2s_3(2,2))
		,"T2s(i,j)*T2s(l,m)(1,1,2,2)");
  test_for_zero(t4ddg_2(1,2,0,0) - (t2s_2(1,2)*t2s_3(0,0))
		,"T2s(i,j)*T2s(l,m)(1,2,0,0)");
  test_for_zero(t4ddg_2(1,2,0,1) - (t2s_2(1,2)*t2s_3(0,1))
		,"T2s(i,j)*T2s(l,m)(1,2,0,1)");
  test_for_zero(t4ddg_2(1,2,0,2) - (t2s_2(1,2)*t2s_3(0,2))
		,"T2s(i,j)*T2s(l,m)(1,2,0,2)");
  test_for_zero(t4ddg_2(1,2,1,0) - (t2s_2(1,2)*t2s_3(1,0))
		,"T2s(i,j)*T2s(l,m)(1,2,1,0)");
  test_for_zero(t4ddg_2(1,2,1,1) - (t2s_2(1,2)*t2s_3(1,1))
		,"T2s(i,j)*T2s(l,m)(1,2,1,1)");
  test_for_zero(t4ddg_2(1,2,1,2) - (t2s_2(1,2)*t2s_3(1,2))
		,"T2s(i,j)*T2s(l,m)(1,2,1,2)");
  test_for_zero(t4ddg_2(1,2,2,0) - (t2s_2(1,2)*t2s_3(2,0))
		,"T2s(i,j)*T2s(l,m)(1,2,2,0)");
  test_for_zero(t4ddg_2(1,2,2,1) - (t2s_2(1,2)*t2s_3(2,1))
		,"T2s(i,j)*T2s(l,m)(1,2,2,1)");
  test_for_zero(t4ddg_2(1,2,2,2) - (t2s_2(1,2)*t2s_3(2,2))
		,"T2s(i,j)*T2s(l,m)(1,2,2,2)");
  test_for_zero(t4ddg_2(2,0,0,0) - (t2s_2(2,0)*t2s_3(0,0))
		,"T2s(i,j)*T2s(l,m)(2,0,0,0)");
  test_for_zero(t4ddg_2(2,0,0,1) - (t2s_2(2,0)*t2s_3(0,1))
		,"T2s(i,j)*T2s(l,m)(2,0,0,1)");
  test_for_zero(t4ddg_2(2,0,0,2) - (t2s_2(2,0)*t2s_3(0,2))
		,"T2s(i,j)*T2s(l,m)(2,0,0,2)");
  test_for_zero(t4ddg_2(2,0,1,0) - (t2s_2(2,0)*t2s_3(1,0))
		,"T2s(i,j)*T2s(l,m)(2,0,1,0)");
  test_for_zero(t4ddg_2(2,0,1,1) - (t2s_2(2,0)*t2s_3(1,1))
		,"T2s(i,j)*T2s(l,m)(2,0,1,1)");
  test_for_zero(t4ddg_2(2,0,1,2) - (t2s_2(2,0)*t2s_3(1,2))
		,"T2s(i,j)*T2s(l,m)(2,0,1,2)");
  test_for_zero(t4ddg_2(2,0,2,0) - (t2s_2(2,0)*t2s_3(2,0))
		,"T2s(i,j)*T2s(l,m)(2,0,2,0)");
  test_for_zero(t4ddg_2(2,0,2,1) - (t2s_2(2,0)*t2s_3(2,1))
		,"T2s(i,j)*T2s(l,m)(2,0,2,1)");
  test_for_zero(t4ddg_2(2,0,2,2) - (t2s_2(2,0)*t2s_3(2,2))
		,"T2s(i,j)*T2s(l,m)(2,0,2,2)");
  test_for_zero(t4ddg_2(2,1,0,0) - (t2s_2(2,1)*t2s_3(0,0))
		,"T2s(i,j)*T2s(l,m)(2,1,0,0)");
  test_for_zero(t4ddg_2(2,1,0,1) - (t2s_2(2,1)*t2s_3(0,1))
		,"T2s(i,j)*T2s(l,m)(2,1,0,1)");
  test_for_zero(t4ddg_2(2,1,0,2) - (t2s_2(2,1)*t2s_3(0,2))
		,"T2s(i,j)*T2s(l,m)(2,1,0,2)");
  test_for_zero(t4ddg_2(2,1,1,0) - (t2s_2(2,1)*t2s_3(1,0))
		,"T2s(i,j)*T2s(l,m)(2,1,1,0)");
  test_for_zero(t4ddg_2(2,1,1,1) - (t2s_2(2,1)*t2s_3(1,1))
		,"T2s(i,j)*T2s(l,m)(2,1,1,1)");
  test_for_zero(t4ddg_2(2,1,1,2) - (t2s_2(2,1)*t2s_3(1,2))
		,"T2s(i,j)*T2s(l,m)(2,1,1,2)");
  test_for_zero(t4ddg_2(2,1,2,0) - (t2s_2(2,1)*t2s_3(2,0))
		,"T2s(i,j)*T2s(l,m)(2,1,2,0)");
  test_for_zero(t4ddg_2(2,1,2,1) - (t2s_2(2,1)*t2s_3(2,1))
		,"T2s(i,j)*T2s(l,m)(2,1,2,1)");
  test_for_zero(t4ddg_2(2,1,2,2) - (t2s_2(2,1)*t2s_3(2,2))
		,"T2s(i,j)*T2s(l,m)(2,1,2,2)");
  test_for_zero(t4ddg_2(2,2,0,0) - (t2s_2(2,2)*t2s_3(0,0))
		,"T2s(i,j)*T2s(l,m)(2,2,0,0)");
  test_for_zero(t4ddg_2(2,2,0,1) - (t2s_2(2,2)*t2s_3(0,1))
		,"T2s(i,j)*T2s(l,m)(2,2,0,1)");
  test_for_zero(t4ddg_2(2,2,0,2) - (t2s_2(2,2)*t2s_3(0,2))
		,"T2s(i,j)*T2s(l,m)(2,2,0,2)");
  test_for_zero(t4ddg_2(2,2,1,0) - (t2s_2(2,2)*t2s_3(1,0))
		,"T2s(i,j)*T2s(l,m)(2,2,1,0)");
  test_for_zero(t4ddg_2(2,2,1,1) - (t2s_2(2,2)*t2s_3(1,1))
		,"T2s(i,j)*T2s(l,m)(2,2,1,1)");
  test_for_zero(t4ddg_2(2,2,1,2) - (t2s_2(2,2)*t2s_3(1,2))
		,"T2s(i,j)*T2s(l,m)(2,2,1,2)");
  test_for_zero(t4ddg_2(2,2,2,0) - (t2s_2(2,2)*t2s_3(2,0))
		,"T2s(i,j)*T2s(l,m)(2,2,2,0)");
  test_for_zero(t4ddg_2(2,2,2,1) - (t2s_2(2,2)*t2s_3(2,1))
		,"T2s(i,j)*T2s(l,m)(2,2,2,1)");
  test_for_zero(t4ddg_2(2,2,2,2) - (t2s_2(2,2)*t2s_3(2,2))
		,"T2s(i,j)*T2s(l,m)(2,2,2,2)");

  test_for_zero(t4ddg_1(i,j,k,l)*t4ddg_2(i,k,j,l)
		- t4ddg_1(0,0,0,0)*t4ddg_2(0,0,0,0)
		- t4ddg_1(0,0,0,1)*t4ddg_2(0,0,0,1)
		- t4ddg_1(0,0,0,2)*t4ddg_2(0,0,0,2)
		- t4ddg_1(0,0,1,0)*t4ddg_2(0,1,0,0)
		- t4ddg_1(0,0,1,1)*t4ddg_2(0,1,0,1)
		- t4ddg_1(0,0,1,2)*t4ddg_2(0,1,0,2)
		- t4ddg_1(0,0,2,0)*t4ddg_2(0,2,0,0)
		- t4ddg_1(0,0,2,1)*t4ddg_2(0,2,0,1)
		- t4ddg_1(0,0,2,2)*t4ddg_2(0,2,0,2)
		- t4ddg_1(0,1,0,0)*t4ddg_2(0,0,1,0)
		- t4ddg_1(0,1,0,1)*t4ddg_2(0,0,1,1)
		- t4ddg_1(0,1,0,2)*t4ddg_2(0,0,1,2)
		- t4ddg_1(0,1,1,0)*t4ddg_2(0,1,1,0)
		- t4ddg_1(0,1,1,1)*t4ddg_2(0,1,1,1)
		- t4ddg_1(0,1,1,2)*t4ddg_2(0,1,1,2)
		- t4ddg_1(0,1,2,0)*t4ddg_2(0,2,1,0)
		- t4ddg_1(0,1,2,1)*t4ddg_2(0,2,1,1)
		- t4ddg_1(0,1,2,2)*t4ddg_2(0,2,1,2)
		- t4ddg_1(0,2,0,0)*t4ddg_2(0,0,2,0)
		- t4ddg_1(0,2,0,1)*t4ddg_2(0,0,2,1)
		- t4ddg_1(0,2,0,2)*t4ddg_2(0,0,2,2)
		- t4ddg_1(0,2,1,0)*t4ddg_2(0,1,2,0)
		- t4ddg_1(0,2,1,1)*t4ddg_2(0,1,2,1)
		- t4ddg_1(0,2,1,2)*t4ddg_2(0,1,2,2)
		- t4ddg_1(0,2,2,0)*t4ddg_2(0,2,2,0)
		- t4ddg_1(0,2,2,1)*t4ddg_2(0,2,2,1)
		- t4ddg_1(0,2,2,2)*t4ddg_2(0,2,2,2)

		- t4ddg_1(1,0,0,0)*t4ddg_2(1,0,0,0)
		- t4ddg_1(1,0,0,1)*t4ddg_2(1,0,0,1)
		- t4ddg_1(1,0,0,2)*t4ddg_2(1,0,0,2)
		- t4ddg_1(1,0,1,0)*t4ddg_2(1,1,0,0)
		- t4ddg_1(1,0,1,1)*t4ddg_2(1,1,0,1)
		- t4ddg_1(1,0,1,2)*t4ddg_2(1,1,0,2)
		- t4ddg_1(1,0,2,0)*t4ddg_2(1,2,0,0)
		- t4ddg_1(1,0,2,1)*t4ddg_2(1,2,0,1)
		- t4ddg_1(1,0,2,2)*t4ddg_2(1,2,0,2)
		- t4ddg_1(1,1,0,0)*t4ddg_2(1,0,1,0)
		- t4ddg_1(1,1,0,1)*t4ddg_2(1,0,1,1)
		- t4ddg_1(1,1,0,2)*t4ddg_2(1,0,1,2)
		- t4ddg_1(1,1,1,0)*t4ddg_2(1,1,1,0)
		- t4ddg_1(1,1,1,1)*t4ddg_2(1,1,1,1)
		- t4ddg_1(1,1,1,2)*t4ddg_2(1,1,1,2)
		- t4ddg_1(1,1,2,0)*t4ddg_2(1,2,1,0)
		- t4ddg_1(1,1,2,1)*t4ddg_2(1,2,1,1)
		- t4ddg_1(1,1,2,2)*t4ddg_2(1,2,1,2)
		- t4ddg_1(1,2,0,0)*t4ddg_2(1,0,2,0)
		- t4ddg_1(1,2,0,1)*t4ddg_2(1,0,2,1)
		- t4ddg_1(1,2,0,2)*t4ddg_2(1,0,2,2)
		- t4ddg_1(1,2,1,0)*t4ddg_2(1,1,2,0)
		- t4ddg_1(1,2,1,1)*t4ddg_2(1,1,2,1)
		- t4ddg_1(1,2,1,2)*t4ddg_2(1,1,2,2)
		- t4ddg_1(1,2,2,0)*t4ddg_2(1,2,2,0)
		- t4ddg_1(1,2,2,1)*t4ddg_2(1,2,2,1)
		- t4ddg_1(1,2,2,2)*t4ddg_2(1,2,2,2)

		- t4ddg_1(2,0,0,0)*t4ddg_2(2,0,0,0)
		- t4ddg_1(2,0,0,1)*t4ddg_2(2,0,0,1)
		- t4ddg_1(2,0,0,2)*t4ddg_2(2,0,0,2)
		- t4ddg_1(2,0,1,0)*t4ddg_2(2,1,0,0)
		- t4ddg_1(2,0,1,1)*t4ddg_2(2,1,0,1)
		- t4ddg_1(2,0,1,2)*t4ddg_2(2,1,0,2)
		- t4ddg_1(2,0,2,0)*t4ddg_2(2,2,0,0)
		- t4ddg_1(2,0,2,1)*t4ddg_2(2,2,0,1)
		- t4ddg_1(2,0,2,2)*t4ddg_2(2,2,0,2)
		- t4ddg_1(2,1,0,0)*t4ddg_2(2,0,1,0)
		- t4ddg_1(2,1,0,1)*t4ddg_2(2,0,1,1)
		- t4ddg_1(2,1,0,2)*t4ddg_2(2,0,1,2)
		- t4ddg_1(2,1,1,0)*t4ddg_2(2,1,1,0)
		- t4ddg_1(2,1,1,1)*t4ddg_2(2,1,1,1)
		- t4ddg_1(2,1,1,2)*t4ddg_2(2,1,1,2)
		- t4ddg_1(2,1,2,0)*t4ddg_2(2,2,1,0)
		- t4ddg_1(2,1,2,1)*t4ddg_2(2,2,1,1)
		- t4ddg_1(2,1,2,2)*t4ddg_2(2,2,1,2)
		- t4ddg_1(2,2,0,0)*t4ddg_2(2,0,2,0)
		- t4ddg_1(2,2,0,1)*t4ddg_2(2,0,2,1)
		- t4ddg_1(2,2,0,2)*t4ddg_2(2,0,2,2)
		- t4ddg_1(2,2,1,0)*t4ddg_2(2,1,2,0)
		- t4ddg_1(2,2,1,1)*t4ddg_2(2,1,2,1)
		- t4ddg_1(2,2,1,2)*t4ddg_2(2,1,2,2)
		- t4ddg_1(2,2,2,0)*t4ddg_2(2,2,2,0)
		- t4ddg_1(2,2,2,1)*t4ddg_2(2,2,2,1)
		- t4ddg_1(2,2,2,2)*t4ddg_2(2,2,2,2)
		,"T4ddg(i,j,k,l)*T4ddg(i,j,k,l)");

  t4ddg_1(i,j,k,l)=t4ddg_2(i,j,k,l)+t4ddg_3(i,j,k,l);
  test_for_zero(t4ddg_1(0,0,0,0) - (t4ddg_2(0,0,0,0)+t4ddg_3(0,0,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,0,0,0)");
  test_for_zero(t4ddg_1(0,0,0,1) - (t4ddg_2(0,0,0,1)+t4ddg_3(0,0,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,0,0,1)");
  test_for_zero(t4ddg_1(0,0,0,2) - (t4ddg_2(0,0,0,2)+t4ddg_3(0,0,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,0,0,2)");
  test_for_zero(t4ddg_1(0,0,1,0) - (t4ddg_2(0,0,1,0)+t4ddg_3(0,0,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,0,1,0)");
  test_for_zero(t4ddg_1(0,0,1,1) - (t4ddg_2(0,0,1,1)+t4ddg_3(0,0,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,0,1,1)");
  test_for_zero(t4ddg_1(0,0,1,2) - (t4ddg_2(0,0,1,2)+t4ddg_3(0,0,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,0,1,2)");
  test_for_zero(t4ddg_1(0,0,2,0) - (t4ddg_2(0,0,2,0)+t4ddg_3(0,0,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,0,2,0)");
  test_for_zero(t4ddg_1(0,0,2,1) - (t4ddg_2(0,0,2,1)+t4ddg_3(0,0,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,0,2,1)");
  test_for_zero(t4ddg_1(0,0,2,2) - (t4ddg_2(0,0,2,2)+t4ddg_3(0,0,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,0,2,2)");
  test_for_zero(t4ddg_1(0,1,0,0) - (t4ddg_2(0,1,0,0)+t4ddg_3(0,1,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,1,0,0)");
  test_for_zero(t4ddg_1(0,1,0,1) - (t4ddg_2(0,1,0,1)+t4ddg_3(0,1,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,1,0,1)");
  test_for_zero(t4ddg_1(0,1,0,2) - (t4ddg_2(0,1,0,2)+t4ddg_3(0,1,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,1,0,2)");
  test_for_zero(t4ddg_1(0,1,1,0) - (t4ddg_2(0,1,1,0)+t4ddg_3(0,1,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,1,1,0)");
  test_for_zero(t4ddg_1(0,1,1,1) - (t4ddg_2(0,1,1,1)+t4ddg_3(0,1,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,1,1,1)");
  test_for_zero(t4ddg_1(0,1,1,2) - (t4ddg_2(0,1,1,2)+t4ddg_3(0,1,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,1,1,2)");
  test_for_zero(t4ddg_1(0,1,2,0) - (t4ddg_2(0,1,2,0)+t4ddg_3(0,1,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,1,2,0)");
  test_for_zero(t4ddg_1(0,1,2,1) - (t4ddg_2(0,1,2,1)+t4ddg_3(0,1,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,1,2,1)");
  test_for_zero(t4ddg_1(0,1,2,2) - (t4ddg_2(0,1,2,2)+t4ddg_3(0,1,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,1,2,2)");
  test_for_zero(t4ddg_1(0,2,0,0) - (t4ddg_2(0,2,0,0)+t4ddg_3(0,2,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,2,0,0)");
  test_for_zero(t4ddg_1(0,2,0,1) - (t4ddg_2(0,2,0,1)+t4ddg_3(0,2,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,2,0,1)");
  test_for_zero(t4ddg_1(0,2,0,2) - (t4ddg_2(0,2,0,2)+t4ddg_3(0,2,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,2,0,2)");
  test_for_zero(t4ddg_1(0,2,1,0) - (t4ddg_2(0,2,1,0)+t4ddg_3(0,2,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,2,1,0)");
  test_for_zero(t4ddg_1(0,2,1,1) - (t4ddg_2(0,2,1,1)+t4ddg_3(0,2,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,2,1,1)");
  test_for_zero(t4ddg_1(0,2,1,2) - (t4ddg_2(0,2,1,2)+t4ddg_3(0,2,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,2,1,2)");
  test_for_zero(t4ddg_1(0,2,2,0) - (t4ddg_2(0,2,2,0)+t4ddg_3(0,2,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,2,2,0)");
  test_for_zero(t4ddg_1(0,2,2,1) - (t4ddg_2(0,2,2,1)+t4ddg_3(0,2,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,2,2,1)");
  test_for_zero(t4ddg_1(0,2,2,2) - (t4ddg_2(0,2,2,2)+t4ddg_3(0,2,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(0,2,2,2)");
  test_for_zero(t4ddg_1(1,0,0,0) - (t4ddg_2(1,0,0,0)+t4ddg_3(1,0,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,0,0,0)");
  test_for_zero(t4ddg_1(1,0,0,1) - (t4ddg_2(1,0,0,1)+t4ddg_3(1,0,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,0,0,1)");
  test_for_zero(t4ddg_1(1,0,0,2) - (t4ddg_2(1,0,0,2)+t4ddg_3(1,0,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,0,0,2)");
  test_for_zero(t4ddg_1(1,0,1,0) - (t4ddg_2(1,0,1,0)+t4ddg_3(1,0,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,0,1,0)");
  test_for_zero(t4ddg_1(1,0,1,1) - (t4ddg_2(1,0,1,1)+t4ddg_3(1,0,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,0,1,1)");
  test_for_zero(t4ddg_1(1,0,1,2) - (t4ddg_2(1,0,1,2)+t4ddg_3(1,0,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,0,1,2)");
  test_for_zero(t4ddg_1(1,0,2,0) - (t4ddg_2(1,0,2,0)+t4ddg_3(1,0,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,0,2,0)");
  test_for_zero(t4ddg_1(1,0,2,1) - (t4ddg_2(1,0,2,1)+t4ddg_3(1,0,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,0,2,1)");
  test_for_zero(t4ddg_1(1,0,2,2) - (t4ddg_2(1,0,2,2)+t4ddg_3(1,0,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,0,2,2)");
  test_for_zero(t4ddg_1(1,1,0,0) - (t4ddg_2(1,1,0,0)+t4ddg_3(1,1,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,1,0,0)");
  test_for_zero(t4ddg_1(1,1,0,1) - (t4ddg_2(1,1,0,1)+t4ddg_3(1,1,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,1,0,1)");
  test_for_zero(t4ddg_1(1,1,0,2) - (t4ddg_2(1,1,0,2)+t4ddg_3(1,1,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,1,0,2)");
  test_for_zero(t4ddg_1(1,1,1,0) - (t4ddg_2(1,1,1,0)+t4ddg_3(1,1,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,1,1,0)");
  test_for_zero(t4ddg_1(1,1,1,1) - (t4ddg_2(1,1,1,1)+t4ddg_3(1,1,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,1,1,1)");
  test_for_zero(t4ddg_1(1,1,1,2) - (t4ddg_2(1,1,1,2)+t4ddg_3(1,1,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,1,1,2)");
  test_for_zero(t4ddg_1(1,1,2,0) - (t4ddg_2(1,1,2,0)+t4ddg_3(1,1,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,1,2,0)");
  test_for_zero(t4ddg_1(1,1,2,1) - (t4ddg_2(1,1,2,1)+t4ddg_3(1,1,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,1,2,1)");
  test_for_zero(t4ddg_1(1,1,2,2) - (t4ddg_2(1,1,2,2)+t4ddg_3(1,1,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,1,2,2)");
  test_for_zero(t4ddg_1(1,2,0,0) - (t4ddg_2(1,2,0,0)+t4ddg_3(1,2,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,2,0,0)");
  test_for_zero(t4ddg_1(1,2,0,1) - (t4ddg_2(1,2,0,1)+t4ddg_3(1,2,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,2,0,1)");
  test_for_zero(t4ddg_1(1,2,0,2) - (t4ddg_2(1,2,0,2)+t4ddg_3(1,2,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,2,0,2)");
  test_for_zero(t4ddg_1(1,2,1,0) - (t4ddg_2(1,2,1,0)+t4ddg_3(1,2,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,2,1,0)");
  test_for_zero(t4ddg_1(1,2,1,1) - (t4ddg_2(1,2,1,1)+t4ddg_3(1,2,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,2,1,1)");
  test_for_zero(t4ddg_1(1,2,1,2) - (t4ddg_2(1,2,1,2)+t4ddg_3(1,2,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,2,1,2)");
  test_for_zero(t4ddg_1(1,2,2,0) - (t4ddg_2(1,2,2,0)+t4ddg_3(1,2,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,2,2,0)");
  test_for_zero(t4ddg_1(1,2,2,1) - (t4ddg_2(1,2,2,1)+t4ddg_3(1,2,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,2,2,1)");
  test_for_zero(t4ddg_1(1,2,2,2) - (t4ddg_2(1,2,2,2)+t4ddg_3(1,2,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(1,2,2,2)");
  test_for_zero(t4ddg_1(2,0,0,0) - (t4ddg_2(2,0,0,0)+t4ddg_3(2,0,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,0,0,0)");
  test_for_zero(t4ddg_1(2,0,0,1) - (t4ddg_2(2,0,0,1)+t4ddg_3(2,0,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,0,0,1)");
  test_for_zero(t4ddg_1(2,0,0,2) - (t4ddg_2(2,0,0,2)+t4ddg_3(2,0,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,0,0,2)");
  test_for_zero(t4ddg_1(2,0,1,0) - (t4ddg_2(2,0,1,0)+t4ddg_3(2,0,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,0,1,0)");
  test_for_zero(t4ddg_1(2,0,1,1) - (t4ddg_2(2,0,1,1)+t4ddg_3(2,0,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,0,1,1)");
  test_for_zero(t4ddg_1(2,0,1,2) - (t4ddg_2(2,0,1,2)+t4ddg_3(2,0,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,0,1,2)");
  test_for_zero(t4ddg_1(2,0,2,0) - (t4ddg_2(2,0,2,0)+t4ddg_3(2,0,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,0,2,0)");
  test_for_zero(t4ddg_1(2,0,2,1) - (t4ddg_2(2,0,2,1)+t4ddg_3(2,0,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,0,2,1)");
  test_for_zero(t4ddg_1(2,0,2,2) - (t4ddg_2(2,0,2,2)+t4ddg_3(2,0,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,0,2,2)");
  test_for_zero(t4ddg_1(2,1,0,0) - (t4ddg_2(2,1,0,0)+t4ddg_3(2,1,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,1,0,0)");
  test_for_zero(t4ddg_1(2,1,0,1) - (t4ddg_2(2,1,0,1)+t4ddg_3(2,1,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,1,0,1)");
  test_for_zero(t4ddg_1(2,1,0,2) - (t4ddg_2(2,1,0,2)+t4ddg_3(2,1,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,1,0,2)");
  test_for_zero(t4ddg_1(2,1,1,0) - (t4ddg_2(2,1,1,0)+t4ddg_3(2,1,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,1,1,0)");
  test_for_zero(t4ddg_1(2,1,1,1) - (t4ddg_2(2,1,1,1)+t4ddg_3(2,1,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,1,1,1)");
  test_for_zero(t4ddg_1(2,1,1,2) - (t4ddg_2(2,1,1,2)+t4ddg_3(2,1,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,1,1,2)");
  test_for_zero(t4ddg_1(2,1,2,0) - (t4ddg_2(2,1,2,0)+t4ddg_3(2,1,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,1,2,0)");
  test_for_zero(t4ddg_1(2,1,2,1) - (t4ddg_2(2,1,2,1)+t4ddg_3(2,1,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,1,2,1)");
  test_for_zero(t4ddg_1(2,1,2,2) - (t4ddg_2(2,1,2,2)+t4ddg_3(2,1,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,1,2,2)");
  test_for_zero(t4ddg_1(2,2,0,0) - (t4ddg_2(2,2,0,0)+t4ddg_3(2,2,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,2,0,0)");
  test_for_zero(t4ddg_1(2,2,0,1) - (t4ddg_2(2,2,0,1)+t4ddg_3(2,2,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,2,0,1)");
  test_for_zero(t4ddg_1(2,2,0,2) - (t4ddg_2(2,2,0,2)+t4ddg_3(2,2,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,2,0,2)");
  test_for_zero(t4ddg_1(2,2,1,0) - (t4ddg_2(2,2,1,0)+t4ddg_3(2,2,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,2,1,0)");
  test_for_zero(t4ddg_1(2,2,1,1) - (t4ddg_2(2,2,1,1)+t4ddg_3(2,2,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,2,1,1)");
  test_for_zero(t4ddg_1(2,2,1,2) - (t4ddg_2(2,2,1,2)+t4ddg_3(2,2,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,2,1,2)");
  test_for_zero(t4ddg_1(2,2,2,0) - (t4ddg_2(2,2,2,0)+t4ddg_3(2,2,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,2,2,0)");
  test_for_zero(t4ddg_1(2,2,2,1) - (t4ddg_2(2,2,2,1)+t4ddg_3(2,2,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,2,2,1)");
  test_for_zero(t4ddg_1(2,2,2,2) - (t4ddg_2(2,2,2,2)+t4ddg_3(2,2,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(i,j,k,l)(2,2,2,2)");

  t4ddg_1(i,j,k,l)=t4ddg_2(i,j,k,l)+t4ddg_3(k,l,i,j);
  test_for_zero(t4ddg_1(0,0,0,0) - (t4ddg_2(0,0,0,0)+t4ddg_3(0,0,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,0,0,0)");
  test_for_zero(t4ddg_1(0,0,0,1) - (t4ddg_2(0,0,0,1)+t4ddg_3(0,1,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,0,0,1)");
  test_for_zero(t4ddg_1(0,0,0,2) - (t4ddg_2(0,0,0,2)+t4ddg_3(0,2,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,0,0,2)");
  test_for_zero(t4ddg_1(0,0,1,0) - (t4ddg_2(0,0,1,0)+t4ddg_3(1,0,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,0,1,0)");
  test_for_zero(t4ddg_1(0,0,1,1) - (t4ddg_2(0,0,1,1)+t4ddg_3(1,1,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,0,1,1)");
  test_for_zero(t4ddg_1(0,0,1,2) - (t4ddg_2(0,0,1,2)+t4ddg_3(1,2,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,0,1,2)");
  test_for_zero(t4ddg_1(0,0,2,0) - (t4ddg_2(0,0,2,0)+t4ddg_3(2,0,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,0,2,0)");
  test_for_zero(t4ddg_1(0,0,2,1) - (t4ddg_2(0,0,2,1)+t4ddg_3(2,1,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,0,2,1)");
  test_for_zero(t4ddg_1(0,0,2,2) - (t4ddg_2(0,0,2,2)+t4ddg_3(2,2,0,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,0,2,2)");
  test_for_zero(t4ddg_1(0,1,0,0) - (t4ddg_2(0,1,0,0)+t4ddg_3(0,0,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,1,0,0)");
  test_for_zero(t4ddg_1(0,1,0,1) - (t4ddg_2(0,1,0,1)+t4ddg_3(0,1,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,1,0,1)");
  test_for_zero(t4ddg_1(0,1,0,2) - (t4ddg_2(0,1,0,2)+t4ddg_3(0,2,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,1,0,2)");
  test_for_zero(t4ddg_1(0,1,1,0) - (t4ddg_2(0,1,1,0)+t4ddg_3(1,0,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,1,1,0)");
  test_for_zero(t4ddg_1(0,1,1,1) - (t4ddg_2(0,1,1,1)+t4ddg_3(1,1,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,1,1,1)");
  test_for_zero(t4ddg_1(0,1,1,2) - (t4ddg_2(0,1,1,2)+t4ddg_3(1,2,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,1,1,2)");
  test_for_zero(t4ddg_1(0,1,2,0) - (t4ddg_2(0,1,2,0)+t4ddg_3(2,0,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,1,2,0)");
  test_for_zero(t4ddg_1(0,1,2,1) - (t4ddg_2(0,1,2,1)+t4ddg_3(2,1,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,1,2,1)");
  test_for_zero(t4ddg_1(0,1,2,2) - (t4ddg_2(0,1,2,2)+t4ddg_3(2,2,0,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,1,2,2)");
  test_for_zero(t4ddg_1(0,2,0,0) - (t4ddg_2(0,2,0,0)+t4ddg_3(0,0,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,2,0,0)");
  test_for_zero(t4ddg_1(0,2,0,1) - (t4ddg_2(0,2,0,1)+t4ddg_3(0,1,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,2,0,1)");
  test_for_zero(t4ddg_1(0,2,0,2) - (t4ddg_2(0,2,0,2)+t4ddg_3(0,2,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,2,0,2)");
  test_for_zero(t4ddg_1(0,2,1,0) - (t4ddg_2(0,2,1,0)+t4ddg_3(1,0,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,2,1,0)");
  test_for_zero(t4ddg_1(0,2,1,1) - (t4ddg_2(0,2,1,1)+t4ddg_3(1,1,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,2,1,1)");
  test_for_zero(t4ddg_1(0,2,1,2) - (t4ddg_2(0,2,1,2)+t4ddg_3(1,2,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,2,1,2)");
  test_for_zero(t4ddg_1(0,2,2,0) - (t4ddg_2(0,2,2,0)+t4ddg_3(2,0,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,2,2,0)");
  test_for_zero(t4ddg_1(0,2,2,1) - (t4ddg_2(0,2,2,1)+t4ddg_3(2,1,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,2,2,1)");
  test_for_zero(t4ddg_1(0,2,2,2) - (t4ddg_2(0,2,2,2)+t4ddg_3(2,2,0,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(0,2,2,2)");
  test_for_zero(t4ddg_1(1,0,0,0) - (t4ddg_2(1,0,0,0)+t4ddg_3(0,0,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,0,0,0)");
  test_for_zero(t4ddg_1(1,0,0,1) - (t4ddg_2(1,0,0,1)+t4ddg_3(0,1,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,0,0,1)");
  test_for_zero(t4ddg_1(1,0,0,2) - (t4ddg_2(1,0,0,2)+t4ddg_3(0,2,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,0,0,2)");
  test_for_zero(t4ddg_1(1,0,1,0) - (t4ddg_2(1,0,1,0)+t4ddg_3(1,0,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,0,1,0)");
  test_for_zero(t4ddg_1(1,0,1,1) - (t4ddg_2(1,0,1,1)+t4ddg_3(1,1,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,0,1,1)");
  test_for_zero(t4ddg_1(1,0,1,2) - (t4ddg_2(1,0,1,2)+t4ddg_3(1,2,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,0,1,2)");
  test_for_zero(t4ddg_1(1,0,2,0) - (t4ddg_2(1,0,2,0)+t4ddg_3(2,0,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,0,2,0)");
  test_for_zero(t4ddg_1(1,0,2,1) - (t4ddg_2(1,0,2,1)+t4ddg_3(2,1,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,0,2,1)");
  test_for_zero(t4ddg_1(1,0,2,2) - (t4ddg_2(1,0,2,2)+t4ddg_3(2,2,1,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,0,2,2)");
  test_for_zero(t4ddg_1(1,1,0,0) - (t4ddg_2(1,1,0,0)+t4ddg_3(0,0,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,1,0,0)");
  test_for_zero(t4ddg_1(1,1,0,1) - (t4ddg_2(1,1,0,1)+t4ddg_3(0,1,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,1,0,1)");
  test_for_zero(t4ddg_1(1,1,0,2) - (t4ddg_2(1,1,0,2)+t4ddg_3(0,2,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,1,0,2)");
  test_for_zero(t4ddg_1(1,1,1,0) - (t4ddg_2(1,1,1,0)+t4ddg_3(1,0,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,1,1,0)");
  test_for_zero(t4ddg_1(1,1,1,1) - (t4ddg_2(1,1,1,1)+t4ddg_3(1,1,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,1,1,1)");
  test_for_zero(t4ddg_1(1,1,1,2) - (t4ddg_2(1,1,1,2)+t4ddg_3(1,2,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,1,1,2)");
  test_for_zero(t4ddg_1(1,1,2,0) - (t4ddg_2(1,1,2,0)+t4ddg_3(2,0,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,1,2,0)");
  test_for_zero(t4ddg_1(1,1,2,1) - (t4ddg_2(1,1,2,1)+t4ddg_3(2,1,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,1,2,1)");
  test_for_zero(t4ddg_1(1,1,2,2) - (t4ddg_2(1,1,2,2)+t4ddg_3(2,2,1,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,1,2,2)");
  test_for_zero(t4ddg_1(1,2,0,0) - (t4ddg_2(1,2,0,0)+t4ddg_3(0,0,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,2,0,0)");
  test_for_zero(t4ddg_1(1,2,0,1) - (t4ddg_2(1,2,0,1)+t4ddg_3(0,1,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,2,0,1)");
  test_for_zero(t4ddg_1(1,2,0,2) - (t4ddg_2(1,2,0,2)+t4ddg_3(0,2,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,2,0,2)");
  test_for_zero(t4ddg_1(1,2,1,0) - (t4ddg_2(1,2,1,0)+t4ddg_3(1,0,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,2,1,0)");
  test_for_zero(t4ddg_1(1,2,1,1) - (t4ddg_2(1,2,1,1)+t4ddg_3(1,1,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,2,1,1)");
  test_for_zero(t4ddg_1(1,2,1,2) - (t4ddg_2(1,2,1,2)+t4ddg_3(1,2,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,2,1,2)");
  test_for_zero(t4ddg_1(1,2,2,0) - (t4ddg_2(1,2,2,0)+t4ddg_3(2,0,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,2,2,0)");
  test_for_zero(t4ddg_1(1,2,2,1) - (t4ddg_2(1,2,2,1)+t4ddg_3(2,1,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,2,2,1)");
  test_for_zero(t4ddg_1(1,2,2,2) - (t4ddg_2(1,2,2,2)+t4ddg_3(2,2,1,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(1,2,2,2)");
  test_for_zero(t4ddg_1(2,0,0,0) - (t4ddg_2(2,0,0,0)+t4ddg_3(0,0,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,0,0,0)");
  test_for_zero(t4ddg_1(2,0,0,1) - (t4ddg_2(2,0,0,1)+t4ddg_3(0,1,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,0,0,1)");
  test_for_zero(t4ddg_1(2,0,0,2) - (t4ddg_2(2,0,0,2)+t4ddg_3(0,2,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,0,0,2)");
  test_for_zero(t4ddg_1(2,0,1,0) - (t4ddg_2(2,0,1,0)+t4ddg_3(1,0,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,0,1,0)");
  test_for_zero(t4ddg_1(2,0,1,1) - (t4ddg_2(2,0,1,1)+t4ddg_3(1,1,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,0,1,1)");
  test_for_zero(t4ddg_1(2,0,1,2) - (t4ddg_2(2,0,1,2)+t4ddg_3(1,2,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,0,1,2)");
  test_for_zero(t4ddg_1(2,0,2,0) - (t4ddg_2(2,0,2,0)+t4ddg_3(2,0,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,0,2,0)");
  test_for_zero(t4ddg_1(2,0,2,1) - (t4ddg_2(2,0,2,1)+t4ddg_3(2,1,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,0,2,1)");
  test_for_zero(t4ddg_1(2,0,2,2) - (t4ddg_2(2,0,2,2)+t4ddg_3(2,2,2,0))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,0,2,2)");
  test_for_zero(t4ddg_1(2,1,0,0) - (t4ddg_2(2,1,0,0)+t4ddg_3(0,0,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,1,0,0)");
  test_for_zero(t4ddg_1(2,1,0,1) - (t4ddg_2(2,1,0,1)+t4ddg_3(0,1,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,1,0,1)");
  test_for_zero(t4ddg_1(2,1,0,2) - (t4ddg_2(2,1,0,2)+t4ddg_3(0,2,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,1,0,2)");
  test_for_zero(t4ddg_1(2,1,1,0) - (t4ddg_2(2,1,1,0)+t4ddg_3(1,0,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,1,1,0)");
  test_for_zero(t4ddg_1(2,1,1,1) - (t4ddg_2(2,1,1,1)+t4ddg_3(1,1,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,1,1,1)");
  test_for_zero(t4ddg_1(2,1,1,2) - (t4ddg_2(2,1,1,2)+t4ddg_3(1,2,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,1,1,2)");
  test_for_zero(t4ddg_1(2,1,2,0) - (t4ddg_2(2,1,2,0)+t4ddg_3(2,0,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,1,2,0)");
  test_for_zero(t4ddg_1(2,1,2,1) - (t4ddg_2(2,1,2,1)+t4ddg_3(2,1,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,1,2,1)");
  test_for_zero(t4ddg_1(2,1,2,2) - (t4ddg_2(2,1,2,2)+t4ddg_3(2,2,2,1))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,1,2,2)");
  test_for_zero(t4ddg_1(2,2,0,0) - (t4ddg_2(2,2,0,0)+t4ddg_3(0,0,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,2,0,0)");
  test_for_zero(t4ddg_1(2,2,0,1) - (t4ddg_2(2,2,0,1)+t4ddg_3(0,1,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,2,0,1)");
  test_for_zero(t4ddg_1(2,2,0,2) - (t4ddg_2(2,2,0,2)+t4ddg_3(0,2,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,2,0,2)");
  test_for_zero(t4ddg_1(2,2,1,0) - (t4ddg_2(2,2,1,0)+t4ddg_3(1,0,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,2,1,0)");
  test_for_zero(t4ddg_1(2,2,1,1) - (t4ddg_2(2,2,1,1)+t4ddg_3(1,1,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,2,1,1)");
  test_for_zero(t4ddg_1(2,2,1,2) - (t4ddg_2(2,2,1,2)+t4ddg_3(1,2,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,2,1,2)");
  test_for_zero(t4ddg_1(2,2,2,0) - (t4ddg_2(2,2,2,0)+t4ddg_3(2,0,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,2,2,0)");
  test_for_zero(t4ddg_1(2,2,2,1) - (t4ddg_2(2,2,2,1)+t4ddg_3(2,1,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,2,2,1)");
  test_for_zero(t4ddg_1(2,2,2,2) - (t4ddg_2(2,2,2,2)+t4ddg_3(2,2,2,2))
		,"T4ddg(i,j,k,l)+T4ddg(k,l,i,j)(2,2,2,2)");


  t4ddg_1(i,j,k,l)=t4ddg_2(i,j,k,l)-t4ddg_3(i,j,k,l);
  test_for_zero(t4ddg_1(0,0,0,0) - (t4ddg_2(0,0,0,0)-t4ddg_3(0,0,0,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,0,0,0)");
  test_for_zero(t4ddg_1(0,0,0,1) - (t4ddg_2(0,0,0,1)-t4ddg_3(0,0,0,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,0,0,1)");
  test_for_zero(t4ddg_1(0,0,0,2) - (t4ddg_2(0,0,0,2)-t4ddg_3(0,0,0,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,0,0,2)");
  test_for_zero(t4ddg_1(0,0,1,0) - (t4ddg_2(0,0,1,0)-t4ddg_3(0,0,1,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,0,1,0)");
  test_for_zero(t4ddg_1(0,0,1,1) - (t4ddg_2(0,0,1,1)-t4ddg_3(0,0,1,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,0,1,1)");
  test_for_zero(t4ddg_1(0,0,1,2) - (t4ddg_2(0,0,1,2)-t4ddg_3(0,0,1,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,0,1,2)");
  test_for_zero(t4ddg_1(0,0,2,0) - (t4ddg_2(0,0,2,0)-t4ddg_3(0,0,2,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,0,2,0)");
  test_for_zero(t4ddg_1(0,0,2,1) - (t4ddg_2(0,0,2,1)-t4ddg_3(0,0,2,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,0,2,1)");
  test_for_zero(t4ddg_1(0,0,2,2) - (t4ddg_2(0,0,2,2)-t4ddg_3(0,0,2,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,0,2,2)");
  test_for_zero(t4ddg_1(0,1,0,0) - (t4ddg_2(0,1,0,0)-t4ddg_3(0,1,0,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,1,0,0)");
  test_for_zero(t4ddg_1(0,1,0,1) - (t4ddg_2(0,1,0,1)-t4ddg_3(0,1,0,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,1,0,1)");
  test_for_zero(t4ddg_1(0,1,0,2) - (t4ddg_2(0,1,0,2)-t4ddg_3(0,1,0,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,1,0,2)");
  test_for_zero(t4ddg_1(0,1,1,0) - (t4ddg_2(0,1,1,0)-t4ddg_3(0,1,1,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,1,1,0)");
  test_for_zero(t4ddg_1(0,1,1,1) - (t4ddg_2(0,1,1,1)-t4ddg_3(0,1,1,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,1,1,1)");
  test_for_zero(t4ddg_1(0,1,1,2) - (t4ddg_2(0,1,1,2)-t4ddg_3(0,1,1,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,1,1,2)");
  test_for_zero(t4ddg_1(0,1,2,0) - (t4ddg_2(0,1,2,0)-t4ddg_3(0,1,2,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,1,2,0)");
  test_for_zero(t4ddg_1(0,1,2,1) - (t4ddg_2(0,1,2,1)-t4ddg_3(0,1,2,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,1,2,1)");
  test_for_zero(t4ddg_1(0,1,2,2) - (t4ddg_2(0,1,2,2)-t4ddg_3(0,1,2,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,1,2,2)");
  test_for_zero(t4ddg_1(0,2,0,0) - (t4ddg_2(0,2,0,0)-t4ddg_3(0,2,0,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,2,0,0)");
  test_for_zero(t4ddg_1(0,2,0,1) - (t4ddg_2(0,2,0,1)-t4ddg_3(0,2,0,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,2,0,1)");
  test_for_zero(t4ddg_1(0,2,0,2) - (t4ddg_2(0,2,0,2)-t4ddg_3(0,2,0,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,2,0,2)");
  test_for_zero(t4ddg_1(0,2,1,0) - (t4ddg_2(0,2,1,0)-t4ddg_3(0,2,1,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,2,1,0)");
  test_for_zero(t4ddg_1(0,2,1,1) - (t4ddg_2(0,2,1,1)-t4ddg_3(0,2,1,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,2,1,1)");
  test_for_zero(t4ddg_1(0,2,1,2) - (t4ddg_2(0,2,1,2)-t4ddg_3(0,2,1,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,2,1,2)");
  test_for_zero(t4ddg_1(0,2,2,0) - (t4ddg_2(0,2,2,0)-t4ddg_3(0,2,2,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,2,2,0)");
  test_for_zero(t4ddg_1(0,2,2,1) - (t4ddg_2(0,2,2,1)-t4ddg_3(0,2,2,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,2,2,1)");
  test_for_zero(t4ddg_1(0,2,2,2) - (t4ddg_2(0,2,2,2)-t4ddg_3(0,2,2,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(0,2,2,2)");
  test_for_zero(t4ddg_1(1,0,0,0) - (t4ddg_2(1,0,0,0)-t4ddg_3(1,0,0,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,0,0,0)");
  test_for_zero(t4ddg_1(1,0,0,1) - (t4ddg_2(1,0,0,1)-t4ddg_3(1,0,0,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,0,0,1)");
  test_for_zero(t4ddg_1(1,0,0,2) - (t4ddg_2(1,0,0,2)-t4ddg_3(1,0,0,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,0,0,2)");
  test_for_zero(t4ddg_1(1,0,1,0) - (t4ddg_2(1,0,1,0)-t4ddg_3(1,0,1,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,0,1,0)");
  test_for_zero(t4ddg_1(1,0,1,1) - (t4ddg_2(1,0,1,1)-t4ddg_3(1,0,1,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,0,1,1)");
  test_for_zero(t4ddg_1(1,0,1,2) - (t4ddg_2(1,0,1,2)-t4ddg_3(1,0,1,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,0,1,2)");
  test_for_zero(t4ddg_1(1,0,2,0) - (t4ddg_2(1,0,2,0)-t4ddg_3(1,0,2,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,0,2,0)");
  test_for_zero(t4ddg_1(1,0,2,1) - (t4ddg_2(1,0,2,1)-t4ddg_3(1,0,2,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,0,2,1)");
  test_for_zero(t4ddg_1(1,0,2,2) - (t4ddg_2(1,0,2,2)-t4ddg_3(1,0,2,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,0,2,2)");
  test_for_zero(t4ddg_1(1,1,0,0) - (t4ddg_2(1,1,0,0)-t4ddg_3(1,1,0,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,1,0,0)");
  test_for_zero(t4ddg_1(1,1,0,1) - (t4ddg_2(1,1,0,1)-t4ddg_3(1,1,0,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,1,0,1)");
  test_for_zero(t4ddg_1(1,1,0,2) - (t4ddg_2(1,1,0,2)-t4ddg_3(1,1,0,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,1,0,2)");
  test_for_zero(t4ddg_1(1,1,1,0) - (t4ddg_2(1,1,1,0)-t4ddg_3(1,1,1,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,1,1,0)");
  test_for_zero(t4ddg_1(1,1,1,1) - (t4ddg_2(1,1,1,1)-t4ddg_3(1,1,1,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,1,1,1)");
  test_for_zero(t4ddg_1(1,1,1,2) - (t4ddg_2(1,1,1,2)-t4ddg_3(1,1,1,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,1,1,2)");
  test_for_zero(t4ddg_1(1,1,2,0) - (t4ddg_2(1,1,2,0)-t4ddg_3(1,1,2,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,1,2,0)");
  test_for_zero(t4ddg_1(1,1,2,1) - (t4ddg_2(1,1,2,1)-t4ddg_3(1,1,2,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,1,2,1)");
  test_for_zero(t4ddg_1(1,1,2,2) - (t4ddg_2(1,1,2,2)-t4ddg_3(1,1,2,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,1,2,2)");
  test_for_zero(t4ddg_1(1,2,0,0) - (t4ddg_2(1,2,0,0)-t4ddg_3(1,2,0,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,2,0,0)");
  test_for_zero(t4ddg_1(1,2,0,1) - (t4ddg_2(1,2,0,1)-t4ddg_3(1,2,0,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,2,0,1)");
  test_for_zero(t4ddg_1(1,2,0,2) - (t4ddg_2(1,2,0,2)-t4ddg_3(1,2,0,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,2,0,2)");
  test_for_zero(t4ddg_1(1,2,1,0) - (t4ddg_2(1,2,1,0)-t4ddg_3(1,2,1,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,2,1,0)");
  test_for_zero(t4ddg_1(1,2,1,1) - (t4ddg_2(1,2,1,1)-t4ddg_3(1,2,1,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,2,1,1)");
  test_for_zero(t4ddg_1(1,2,1,2) - (t4ddg_2(1,2,1,2)-t4ddg_3(1,2,1,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,2,1,2)");
  test_for_zero(t4ddg_1(1,2,2,0) - (t4ddg_2(1,2,2,0)-t4ddg_3(1,2,2,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,2,2,0)");
  test_for_zero(t4ddg_1(1,2,2,1) - (t4ddg_2(1,2,2,1)-t4ddg_3(1,2,2,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,2,2,1)");
  test_for_zero(t4ddg_1(1,2,2,2) - (t4ddg_2(1,2,2,2)-t4ddg_3(1,2,2,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(1,2,2,2)");
  test_for_zero(t4ddg_1(2,0,0,0) - (t4ddg_2(2,0,0,0)-t4ddg_3(2,0,0,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,0,0,0)");
  test_for_zero(t4ddg_1(2,0,0,1) - (t4ddg_2(2,0,0,1)-t4ddg_3(2,0,0,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,0,0,1)");
  test_for_zero(t4ddg_1(2,0,0,2) - (t4ddg_2(2,0,0,2)-t4ddg_3(2,0,0,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,0,0,2)");
  test_for_zero(t4ddg_1(2,0,1,0) - (t4ddg_2(2,0,1,0)-t4ddg_3(2,0,1,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,0,1,0)");
  test_for_zero(t4ddg_1(2,0,1,1) - (t4ddg_2(2,0,1,1)-t4ddg_3(2,0,1,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,0,1,1)");
  test_for_zero(t4ddg_1(2,0,1,2) - (t4ddg_2(2,0,1,2)-t4ddg_3(2,0,1,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,0,1,2)");
  test_for_zero(t4ddg_1(2,0,2,0) - (t4ddg_2(2,0,2,0)-t4ddg_3(2,0,2,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,0,2,0)");
  test_for_zero(t4ddg_1(2,0,2,1) - (t4ddg_2(2,0,2,1)-t4ddg_3(2,0,2,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,0,2,1)");
  test_for_zero(t4ddg_1(2,0,2,2) - (t4ddg_2(2,0,2,2)-t4ddg_3(2,0,2,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,0,2,2)");
  test_for_zero(t4ddg_1(2,1,0,0) - (t4ddg_2(2,1,0,0)-t4ddg_3(2,1,0,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,1,0,0)");
  test_for_zero(t4ddg_1(2,1,0,1) - (t4ddg_2(2,1,0,1)-t4ddg_3(2,1,0,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,1,0,1)");
  test_for_zero(t4ddg_1(2,1,0,2) - (t4ddg_2(2,1,0,2)-t4ddg_3(2,1,0,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,1,0,2)");
  test_for_zero(t4ddg_1(2,1,1,0) - (t4ddg_2(2,1,1,0)-t4ddg_3(2,1,1,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,1,1,0)");
  test_for_zero(t4ddg_1(2,1,1,1) - (t4ddg_2(2,1,1,1)-t4ddg_3(2,1,1,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,1,1,1)");
  test_for_zero(t4ddg_1(2,1,1,2) - (t4ddg_2(2,1,1,2)-t4ddg_3(2,1,1,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,1,1,2)");
  test_for_zero(t4ddg_1(2,1,2,0) - (t4ddg_2(2,1,2,0)-t4ddg_3(2,1,2,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,1,2,0)");
  test_for_zero(t4ddg_1(2,1,2,1) - (t4ddg_2(2,1,2,1)-t4ddg_3(2,1,2,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,1,2,1)");
  test_for_zero(t4ddg_1(2,1,2,2) - (t4ddg_2(2,1,2,2)-t4ddg_3(2,1,2,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,1,2,2)");
  test_for_zero(t4ddg_1(2,2,0,0) - (t4ddg_2(2,2,0,0)-t4ddg_3(2,2,0,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,2,0,0)");
  test_for_zero(t4ddg_1(2,2,0,1) - (t4ddg_2(2,2,0,1)-t4ddg_3(2,2,0,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,2,0,1)");
  test_for_zero(t4ddg_1(2,2,0,2) - (t4ddg_2(2,2,0,2)-t4ddg_3(2,2,0,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,2,0,2)");
  test_for_zero(t4ddg_1(2,2,1,0) - (t4ddg_2(2,2,1,0)-t4ddg_3(2,2,1,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,2,1,0)");
  test_for_zero(t4ddg_1(2,2,1,1) - (t4ddg_2(2,2,1,1)-t4ddg_3(2,2,1,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,2,1,1)");
  test_for_zero(t4ddg_1(2,2,1,2) - (t4ddg_2(2,2,1,2)-t4ddg_3(2,2,1,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,2,1,2)");
  test_for_zero(t4ddg_1(2,2,2,0) - (t4ddg_2(2,2,2,0)-t4ddg_3(2,2,2,0))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,2,2,0)");
  test_for_zero(t4ddg_1(2,2,2,1) - (t4ddg_2(2,2,2,1)-t4ddg_3(2,2,2,1))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,2,2,1)");
  test_for_zero(t4ddg_1(2,2,2,2) - (t4ddg_2(2,2,2,2)-t4ddg_3(2,2,2,2))
		,"T4ddg(i,j,k,l)-T4ddg(i,j,k,l)(2,2,2,2)");

  t4ddg_2(i,k,j,l)=t2s_2(i,k)*t2s_2(j,l);
  t4ddg_3(i,l,j,k)=t2s_2(i,l)*t2s_2(j,k);
  t4ddg_1(i,j,k,l)=(t4ddg_2(i,k,j,l) || t4ddg_3(i,l,j,k));
  test_for_zero(t4ddg_1(0,0,0,0) - (t4ddg_2(0,0,0,0)+t4ddg_3(0,0,0,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,0,0,0)");
  test_for_zero(t4ddg_1(0,0,0,1) - (t4ddg_2(0,0,0,1)+t4ddg_3(0,1,0,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,0,0,1)");
  test_for_zero(t4ddg_1(0,0,0,2) - (t4ddg_2(0,0,0,2)+t4ddg_3(0,2,0,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,0,0,2)");
  test_for_zero(t4ddg_1(0,1,0,0) - (t4ddg_2(0,0,1,0)+t4ddg_3(0,0,1,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,0,1,0)");
  test_for_zero(t4ddg_1(0,1,0,1) - (t4ddg_2(0,0,1,1)+t4ddg_3(0,1,1,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,0,1,1)");
  test_for_zero(t4ddg_1(0,1,0,2) - (t4ddg_2(0,0,1,2)+t4ddg_3(0,2,1,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,0,1,2)");
  test_for_zero(t4ddg_1(0,2,0,0) - (t4ddg_2(0,0,2,0)+t4ddg_3(0,0,2,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,0,2,0)");
  test_for_zero(t4ddg_1(0,2,0,1) - (t4ddg_2(0,0,2,1)+t4ddg_3(0,1,2,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,0,2,1)");
  test_for_zero(t4ddg_1(0,2,0,2) - (t4ddg_2(0,0,2,2)+t4ddg_3(0,2,2,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,0,2,2)");
  test_for_zero(t4ddg_1(0,0,1,0) - (t4ddg_2(0,1,0,0)+t4ddg_3(0,0,0,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,1,0,0)");
  test_for_zero(t4ddg_1(0,0,1,1) - (t4ddg_2(0,1,0,1)+t4ddg_3(0,1,0,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,1,0,1)");
  test_for_zero(t4ddg_1(0,0,1,2) - (t4ddg_2(0,1,0,2)+t4ddg_3(0,2,0,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,1,0,2)");
  test_for_zero(t4ddg_1(0,1,1,0) - (t4ddg_2(0,1,1,0)+t4ddg_3(0,0,1,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,1,1,0)");
  test_for_zero(t4ddg_1(0,1,1,1) - (t4ddg_2(0,1,1,1)+t4ddg_3(0,1,1,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,1,1,1)");
  test_for_zero(t4ddg_1(0,1,1,2) - (t4ddg_2(0,1,1,2)+t4ddg_3(0,2,1,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,1,1,2)");
  test_for_zero(t4ddg_1(0,2,1,0) - (t4ddg_2(0,1,2,0)+t4ddg_3(0,0,2,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,1,2,0)");
  test_for_zero(t4ddg_1(0,2,1,1) - (t4ddg_2(0,1,2,1)+t4ddg_3(0,1,2,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,1,2,1)");
  test_for_zero(t4ddg_1(0,2,1,2) - (t4ddg_2(0,1,2,2)+t4ddg_3(0,2,2,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,1,2,2)");
  test_for_zero(t4ddg_1(0,0,2,0) - (t4ddg_2(0,2,0,0)+t4ddg_3(0,0,0,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,2,0,0)");
  test_for_zero(t4ddg_1(0,0,2,1) - (t4ddg_2(0,2,0,1)+t4ddg_3(0,1,0,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,2,0,1)");
  test_for_zero(t4ddg_1(0,0,2,2) - (t4ddg_2(0,2,0,2)+t4ddg_3(0,2,0,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,2,0,2)");
  test_for_zero(t4ddg_1(0,1,2,0) - (t4ddg_2(0,2,1,0)+t4ddg_3(0,0,1,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,2,1,0)");
  test_for_zero(t4ddg_1(0,1,2,1) - (t4ddg_2(0,2,1,1)+t4ddg_3(0,1,1,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,2,1,1)");
  test_for_zero(t4ddg_1(0,1,2,2) - (t4ddg_2(0,2,1,2)+t4ddg_3(0,2,1,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,2,1,2)");
  test_for_zero(t4ddg_1(0,2,2,0) - (t4ddg_2(0,2,2,0)+t4ddg_3(0,0,2,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,2,2,0)");
  test_for_zero(t4ddg_1(0,2,2,1) - (t4ddg_2(0,2,2,1)+t4ddg_3(0,1,2,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,2,2,1)");
  test_for_zero(t4ddg_1(0,2,2,2) - (t4ddg_2(0,2,2,2)+t4ddg_3(0,2,2,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(0,2,2,2)");
  test_for_zero(t4ddg_1(1,0,0,0) - (t4ddg_2(1,0,0,0)+t4ddg_3(1,0,0,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,0,0,0)");
  test_for_zero(t4ddg_1(1,0,0,1) - (t4ddg_2(1,0,0,1)+t4ddg_3(1,1,0,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,0,0,1)");
  test_for_zero(t4ddg_1(1,0,0,2) - (t4ddg_2(1,0,0,2)+t4ddg_3(1,2,0,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,0,0,2)");
  test_for_zero(t4ddg_1(1,1,0,0) - (t4ddg_2(1,0,1,0)+t4ddg_3(1,0,1,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,0,1,0)");
  test_for_zero(t4ddg_1(1,1,0,1) - (t4ddg_2(1,0,1,1)+t4ddg_3(1,1,1,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,0,1,1)");
  test_for_zero(t4ddg_1(1,1,0,2) - (t4ddg_2(1,0,1,2)+t4ddg_3(1,2,1,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,0,1,2)");
  test_for_zero(t4ddg_1(1,2,0,0) - (t4ddg_2(1,0,2,0)+t4ddg_3(1,0,2,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,0,2,0)");
  test_for_zero(t4ddg_1(1,2,0,1) - (t4ddg_2(1,0,2,1)+t4ddg_3(1,1,2,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,0,2,1)");
  test_for_zero(t4ddg_1(1,2,0,2) - (t4ddg_2(1,0,2,2)+t4ddg_3(1,2,2,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,0,2,2)");
  test_for_zero(t4ddg_1(1,0,1,0) - (t4ddg_2(1,1,0,0)+t4ddg_3(1,0,0,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,1,0,0)");
  test_for_zero(t4ddg_1(1,0,1,1) - (t4ddg_2(1,1,0,1)+t4ddg_3(1,1,0,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,1,0,1)");
  test_for_zero(t4ddg_1(1,0,1,2) - (t4ddg_2(1,1,0,2)+t4ddg_3(1,2,0,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,1,0,2)");
  test_for_zero(t4ddg_1(1,1,1,0) - (t4ddg_2(1,1,1,0)+t4ddg_3(1,0,1,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,1,1,0)");
  test_for_zero(t4ddg_1(1,1,1,1) - (t4ddg_2(1,1,1,1)+t4ddg_3(1,1,1,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,1,1,1)");
  test_for_zero(t4ddg_1(1,1,1,2) - (t4ddg_2(1,1,1,2)+t4ddg_3(1,2,1,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,1,1,2)");
  test_for_zero(t4ddg_1(1,2,1,0) - (t4ddg_2(1,1,2,0)+t4ddg_3(1,0,2,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,1,2,0)");
  test_for_zero(t4ddg_1(1,2,1,1) - (t4ddg_2(1,1,2,1)+t4ddg_3(1,1,2,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,1,2,1)");
  test_for_zero(t4ddg_1(1,2,1,2) - (t4ddg_2(1,1,2,2)+t4ddg_3(1,2,2,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,1,2,2)");
  test_for_zero(t4ddg_1(1,0,2,0) - (t4ddg_2(1,2,0,0)+t4ddg_3(1,0,0,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,2,0,0)");
  test_for_zero(t4ddg_1(1,0,2,1) - (t4ddg_2(1,2,0,1)+t4ddg_3(1,1,0,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,2,0,1)");
  test_for_zero(t4ddg_1(1,0,2,2) - (t4ddg_2(1,2,0,2)+t4ddg_3(1,2,0,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,2,0,2)");
  test_for_zero(t4ddg_1(1,1,2,0) - (t4ddg_2(1,2,1,0)+t4ddg_3(1,0,1,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,2,1,0)");
  test_for_zero(t4ddg_1(1,1,2,1) - (t4ddg_2(1,2,1,1)+t4ddg_3(1,1,1,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,2,1,1)");
  test_for_zero(t4ddg_1(1,1,2,2) - (t4ddg_2(1,2,1,2)+t4ddg_3(1,2,1,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,2,1,2)");
  test_for_zero(t4ddg_1(1,2,2,0) - (t4ddg_2(1,2,2,0)+t4ddg_3(1,0,2,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,2,2,0)");
  test_for_zero(t4ddg_1(1,2,2,1) - (t4ddg_2(1,2,2,1)+t4ddg_3(1,1,2,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,2,2,1)");
  test_for_zero(t4ddg_1(1,2,2,2) - (t4ddg_2(1,2,2,2)+t4ddg_3(1,2,2,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(1,2,2,2)");
  test_for_zero(t4ddg_1(2,0,0,0) - (t4ddg_2(2,0,0,0)+t4ddg_3(2,0,0,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,0,0,0)");
  test_for_zero(t4ddg_1(2,0,0,1) - (t4ddg_2(2,0,0,1)+t4ddg_3(2,1,0,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,0,0,1)");
  test_for_zero(t4ddg_1(2,0,0,2) - (t4ddg_2(2,0,0,2)+t4ddg_3(2,2,0,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,0,0,2)");
  test_for_zero(t4ddg_1(2,1,0,0) - (t4ddg_2(2,0,1,0)+t4ddg_3(2,0,1,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,0,1,0)");
  test_for_zero(t4ddg_1(2,1,0,1) - (t4ddg_2(2,0,1,1)+t4ddg_3(2,1,1,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,0,1,1)");
  test_for_zero(t4ddg_1(2,1,0,2) - (t4ddg_2(2,0,1,2)+t4ddg_3(2,2,1,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,0,1,2)");
  test_for_zero(t4ddg_1(2,2,0,0) - (t4ddg_2(2,0,2,0)+t4ddg_3(2,0,2,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,0,2,0)");
  test_for_zero(t4ddg_1(2,2,0,1) - (t4ddg_2(2,0,2,1)+t4ddg_3(2,1,2,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,0,2,1)");
  test_for_zero(t4ddg_1(2,2,0,2) - (t4ddg_2(2,0,2,2)+t4ddg_3(2,2,2,0))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,0,2,2)");
  test_for_zero(t4ddg_1(2,0,1,0) - (t4ddg_2(2,1,0,0)+t4ddg_3(2,0,0,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,1,0,0)");
  test_for_zero(t4ddg_1(2,0,1,1) - (t4ddg_2(2,1,0,1)+t4ddg_3(2,1,0,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,1,0,1)");
  test_for_zero(t4ddg_1(2,0,1,2) - (t4ddg_2(2,1,0,2)+t4ddg_3(2,2,0,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,1,0,2)");
  test_for_zero(t4ddg_1(2,1,1,0) - (t4ddg_2(2,1,1,0)+t4ddg_3(2,0,1,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,1,1,0)");
  test_for_zero(t4ddg_1(2,1,1,1) - (t4ddg_2(2,1,1,1)+t4ddg_3(2,1,1,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,1,1,1)");
  test_for_zero(t4ddg_1(2,1,1,2) - (t4ddg_2(2,1,1,2)+t4ddg_3(2,2,1,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,1,1,2)");
  test_for_zero(t4ddg_1(2,2,1,0) - (t4ddg_2(2,1,2,0)+t4ddg_3(2,0,2,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,1,2,0)");
  test_for_zero(t4ddg_1(2,2,1,1) - (t4ddg_2(2,1,2,1)+t4ddg_3(2,1,2,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,1,2,1)");
  test_for_zero(t4ddg_1(2,2,1,2) - (t4ddg_2(2,1,2,2)+t4ddg_3(2,2,2,1))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,1,2,2)");
  test_for_zero(t4ddg_1(2,0,2,0) - (t4ddg_2(2,2,0,0)+t4ddg_3(2,0,0,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,2,0,0)");
  test_for_zero(t4ddg_1(2,0,2,1) - (t4ddg_2(2,2,0,1)+t4ddg_3(2,1,0,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,2,0,1)");
  test_for_zero(t4ddg_1(2,0,2,2) - (t4ddg_2(2,2,0,2)+t4ddg_3(2,2,0,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,2,0,2)");
  test_for_zero(t4ddg_1(2,1,2,0) - (t4ddg_2(2,2,1,0)+t4ddg_3(2,0,1,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,2,1,0)");
  test_for_zero(t4ddg_1(2,1,2,1) - (t4ddg_2(2,2,1,1)+t4ddg_3(2,1,1,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,2,1,1)");
  test_for_zero(t4ddg_1(2,1,2,2) - (t4ddg_2(2,2,1,2)+t4ddg_3(2,2,1,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,2,1,2)");
  test_for_zero(t4ddg_1(2,2,2,0) - (t4ddg_2(2,2,2,0)+t4ddg_3(2,0,2,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,2,2,0)");
  test_for_zero(t4ddg_1(2,2,2,1) - (t4ddg_2(2,2,2,1)+t4ddg_3(2,1,2,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,2,2,1)");
  test_for_zero(t4ddg_1(2,2,2,2) - (t4ddg_2(2,2,2,2)+t4ddg_3(2,2,2,2))
		,"T4ddg(i,k,j,l)||T4ddg(i,l,j,k)(2,2,2,2)");
}

